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Topological Quantum Computation

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Zhenghan Wang

A co-publication of the AMS and CBMS

Topological quantum computation is a computational paradigm based on
topological phases of matter, which are governed by topological quantum
field theories. In this approach, information is stored in the lowest
energy states of many-anyon systems and processed by braiding
non-abelian anyons. The computational answer is accessed by bringing
anyons together and observing the result. Besides its theoretical
esthetic appeal, the practical merit of the topological approach lies in
its error-minimizing hypothetical hardware: topological phases of matter
are fault-avoiding or deaf to most local noises, and unitary gates are
implemented with exponential accuracy. Experimental realizations are
pursued in systems such as fractional quantum Hall liquids and
topological insulators.

This book expands on the author's CBMS lectures on knots and
topological quantum computing and is intended as a primer for
mathematically inclined graduate students. With an emphasis on
introducing basic notions and current research, this book gives the first
coherent account of the field, covering a wide range of topics:
Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion
category theory, topological quantum field theory, anyon theory,
additive approximation of the Jones polynomial, anyonic quantum
computing models, and mathematical models of topological phases of
matter.

A co-publication of the AMS and CBMS.

Readership

Graduate students and research mathematicians interested in
quantum computers, topological quantum field theory.

Topological quantum computation is a computational paradigm based on
topological phases of matter, which are governed by topological quantum
field theories. In this approach, information is stored in the lowest
energy states of many-anyon systems and processed by braiding
non-abelian anyons. The computational answer is accessed by bringing
anyons together and observing the result. Besides its theoretical
esthetic appeal, the practical merit of the topological approach lies in
its error-minimizing hypothetical hardware: topological phases of matter
are fault-avoiding or deaf to most local noises, and unitary gates are
implemented with exponential accuracy. Experimental realizations are
pursued in systems such as fractional quantum Hall liquids and
topological insulators.

This book expands on the author's CBMS lectures on knots and
topological quantum computing and is intended as a primer for
mathematically inclined graduate students. With an emphasis on
introducing basic notions and current research, this book gives the first
coherent account of the field, covering a wide range of topics:
Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion
category theory, topological quantum field theory, anyon theory,
additive approximation of the Jones polynomial, anyonic quantum
computing models, and mathematical models of topological phases of
matter.

A co-publication of the AMS and CBMS.

Book Series Name:
CBMS Regional Conference Series in Mathematics

Volume:
112

Publication Month and Year:
2010-04-21

Copyright Year:
2010

Page Count:
115

Cover Type:
Softcover

Print ISBN-13:
978-0-8218-4930-9

Online ISBN 13:
978-1-4704-1570-9

Print ISSN:
0160-7642

Online ISSN:
0160-7642

Primary MSC:
57;
81;
68;
18

Textbook?:
false

Applied Math?:
true

MAA Book?:
false

Home Page?:
false

Featured?:
false

Sample?:
false

Reference?:
false

Electronic Media?:
false

Apparel or Gift:
false

Publisher (non-AMS):
A co-publication of the AMS and Conference Board of Mathematical Sciences